Rotunda — Round Barn Design

The barn

Diameter

Cow storey

Mow studs above it

Lower pitch

Upper pitch

Break at

Rib rise

Framed rafters

Double the rafters below the break

Silo & curb

Silo diameter

Top curb

The silo carries the peak Mow floor over the cow storey Post ring under the mow floor Knee brace across the knuckle

Fraser's rafters "were cut to rest on the plate of the silo" — the silo is a mast that runs from the stable floor through the peak, not a drum sitting on the roof. Switch it off the peak and a compression curb appears instead. Pull the post ring out and the mow joists have to span the whole radius, which is why his 2 × 12s land on 4 × 4s at the stanchions.

The plan (Fraser's rings)

Manger

Cow platform

Gutter

Litter alley

Stall width

Cross passages

The feed alley is whatever is left between the silo and the manger, so the rings always close on the diameter you asked for. Cows are counted where the bulletin counts them — on the circle at the rear of the platform, at 3'-6" each.

Loads

Snow (on plan)

Roof dead (on slope)

Hay in the mow

Hay density

Sheathing hoops

Fraser hoops his studs five feet apart and boards over them, so a 20-foot 2 × 6 buckles between hoops and not over the whole storey — 6,750 lb instead of 422. Wind the hoops out to the full height to see the bare-frame answer.

Roof loads are spread over the wedge — a rafter's tributary width is r·Δθ, so the load grows as you walk out toward the eave, and near the peak it is almost nothing. Hay fills the mow to the depth you set or to the roof line above it, whichever comes first.

The deck as a hoop

Roof boards work as a hoop

Board thickness

Hoop efficiency

Rings and rafters alone make a basket: the thrust has nowhere to go but the two end rings. Boards sprung around the cone make it closer to a shell — every board is a hoop. Turn this on and watch the top curb's compression collapse. The efficiency is a modelling knob, not a measurement: butted, lapped boards are nothing like a continuous steel hoop, and 1.0 is the shell limit, not a claim.

Timber

Plate plies

Sill plies

Top curb plies

A ring plate is boards sprung around the circle, not a sawn timber — you cannot bend a 2 × 10 to a 60-foot arc. Fraser's plate is five 1 × 4s; his sill is a 6 × 6 built up out of 1 × 6s, which "forms a continuous hoop around the barn".

Size the framing

Target utilization1.00

Walks each member group's lumber ladder to the lightest section that meets the target, re-solving as the load redistributes — Armature's optimizer, restricted to the barn's own framing. The ring plates are yours to choose; the sizer never touches them.

Display

Exaggerationauto

Peak-value labels

Export

The OBJ is the whole barn, not one rib: every rafter revolved into place and every ring closed on itself, ready to open in Rhino. The CSV carries the ring schedule, every member's forces and the takeoff.

Analyze in Proving Ground revolves the section into a closed massing solid — the envelope plus the silo standing clear through the peak — and hands it over in metres, so the site forces (sun on that big conical roof, wind round a cylinder, envelope carbon, light on the floor) judge the barn you just sized. Rotunda answers a structural question; Proving Ground answers a site one, about the same building.

What this is not

Shares with professional analysis: a genuine first-order plane-frame FE solve (Armature's engine, imported not copied), real dressed lumber sections, self-weight from those sections, utilization with a Euler check, and axisymmetric load and ring mechanics that are exact within the model.

Does not have: wind on the structure (it is the one load that is not axisymmetric — the comparison in the readout is a global drag figure, not a solve); second-order and buckling of the ring itself (a compression ring can buckle out of round, and nothing here checks that); connection and splice design, which is where a round barn's plate actually fails; γ-factors and code load combinations (γ = 1 on characteristic strengths); and a licensed engineer who signs it.

Sources & method

The wedge. Each rib carries a wedge of angle 2π/n, so an areal load q becomes a member load q·r·(2π/n) that grows linearly with radius. Because that is linear in r and r runs linearly along a straight member, evaluating it at each segment's midpoint integrates the wedge exactly — the total applied load matches q·π(R²−r²) to machine precision at any segment count, which the self-test pins.

The rings. n ribs pushing radially with force P on a ring of radius r give hoop force T = P / (2·sin(π/n)) — exact polygon statics, tending to P·n/2π. Each ring enters the FE model as one pin-ended tie from the ring node to a fixed node on the axis, with the area that reproduces the ring's real radial stiffness; the tie's axial force is P, and the ring grows by T·r/(EA). Nothing is fudged and no degree of freedom is invented. Ring ties are excluded from the takeoff, the mass and the sizer — they are the ring, not timber you order.

The joints. A barn is a bearing structure, not a moment frame: rafter feet birdsmouth the plate, joists bear on a ledger, posts carry the plate. Every junction between elements is released; each element stays continuous through its own length. The gambrel break is left rigid on purpose (it is a gusseted splice) — the knee-brace toggle shows how much you are trusting it. The silo's base is fixed, not pinned: a 14-foot cylinder in a footing cannot hinge.

What the deck-hoop switch changes. Off, the roof is a basket — hoop capacity only where a plate runs, so the thrust must reach one of the two end rings. On, the boards carry hoop where the load is generated and the model moves toward membrane behaviour: the top curb's force collapses toward the shell answer of zero. Both are honest models of different buildings; the efficiency slider is where you say which one you are looking at.

The economy. A circle encloses the most floor per lineal foot of wall — even the square of equal area needs 12.8% more (4 ÷ 2√π), and a long two-row barn far more. Fraser put the saving at 34–58% of materials; this tool shows only the wall geometry it rests on, against three rectangles at once, so you can see which comparison is being made.

Wind. Drag F = ½ρV²·C_d·A. A rough cylinder runs C_d ≈ 0.7 against a rectangular building's ≈ 1.3 broadside, and the round barn presents a diameter where the rectangle presents a length. That is Fraser's windstorm claim, and the readout shows it as the ratio of two drag forces with both coefficients stated — not as a structural solve.

The barn. Wilber J. Fraser, Economy of the Round Dairy Barn, University of Illinois Agricultural Experiment Station Bulletin 143 (1910) — Project Gutenberg 38321. The section this tool parameterises is his Fig. 19, but the numbers come from the text, and they are pinned as test fixtures: 188½ lineal feet of wall on a 60-foot barn; 40 cows at 3'-6" at the drop and 2'-10½" at the stanchion; a 9-foot brick cow storey under 20-foot studs, so the plate is 29 feet up; 64 framed rafters, doubled below the break; joists on a post ring at the stanchions over 14- and 8-foot spans; studs hooped every 5 feet; 117,669 cubic feet of content; the equal-area rectangular barn at 36 × 78½ feet holding 42; and $799.76 of lumber at his own prices.

Where this tool reads light. The 1910 bill counts only the members the model solves. Fraser's framing also buys the silo's own studs, headers and purlins between rafters, stanchion and manger framing, door and driveway framing and blocking — so the framing line here comes in under his, and it should. The board and shingle lines are estimated from surface areas, not from a real cutting list.

A polygon is not a circle. This model is n ribs with the siding assumed to hoop continuously around them — true of boards sprung to a circle, false of a barn with flats and corners. Fraser is blunt about the difference: his 16-sided Barn No. 6 "has been racked three times by the wind … yet it is out of plumb at the present time", because "the siding cannot run around the corners". Below a dozen ribs the tool says so.

Buckling is checked on the stick, not the segment. Every run here is chopped into six elements for the solve, and a per-element Euler check would see a 3-foot column where the carpenter sees an 18-foot one. So compression is checked over the whole run, with the unbraced length set by the sheathing hoops — Fraser's are five feet apart, which is the difference between a 20-foot 2 × 6 carrying 422 lb and carrying 6,750. Wind the hoop slider out to see the bare frame.

The mechanics. Matrix displacement method: Hibbeler, Structural Analysis; McGuire, Gallagher & Ziemian, Matrix Structural Analysis — free 2nd ed. Shells of revolution and ring statics: Billington, Thin Shell Concrete Structures. Timber strengths are EN 338 / EN 14080 characteristic values, used as a stand-in for construction-grade softwood; the sections are the real dressed US sizes.